Find the coordinates of point G that lies along the directed line segment from F(-1, -1) to H(-8, 20) and partitions the segment in the ratio of 5:2.

Answer:

The volume of the pyramid is 867 inch^3

Step-by-step explanation:

Here in this question, we are interested in calculating the volume of a square based pyramid.

Mathematically, we can use the formula below to calculate the volume V of a square based pyramid.

V = a^2h/3

where a represents the length of the side of the square and h is the height of the pyramid

From the question, the length of the side of the square is 17 in while the height is 9 in

Plugging these values, we have ;

V = (17^2 * 9)/3 = 17^2 * 3 = 867 cubic inch

Answer:

22 units²

Step-by-step explanation:

1/2b*h=area

You can either count the units or use the distance formula.

[tex]d = \sqrt{ {(x2 - x1)}^{2} + {(y2 - y1)}^{2} } [/tex]

b = 4 units

h = 11 units

area = (1/2*4)*11 = 22 units²

Answer:

It is reduced to the equation of the Theorem of Pythagoras.

Step-by-step explanation:

Any triangle can be modelled by this formula under the Law of Cosine:

[tex]b = \sqrt{a^{2}+c^{2}-2\cdot a\cdot c\cdot \cos B}[/tex]

Where:

[tex]a[/tex], [tex]b[/tex], [tex]c[/tex] - Side lengths, dimensionless.

[tex]B[/tex] - Angle opposed to the side [tex]b[/tex], measured in sexagesimal degrees.

Now, let suppose that angle B is a right angle (90º), so that b is a hypotenuse and a and c are legs. Hence:

[tex]\cos B = 0[/tex]

And the equation is reduced to the form of the Theorem of Pythagoras, that is to say:

[tex]b = \sqrt{a^{2}+c^{2}}[/tex]

Answer:

Step-by-step explanation:

To find the value of h use the formula for finding the slope of a line

That's

[tex]m = \frac{y2 - y1}{x2 - x1} [/tex]

Where ( x1, y1) and (x2 ,y2) are the points

From the question

slope = - 3

The points are [4,-9] and [-3,h]

Substitute these values into the equation

We have

[tex] - 3 = \frac{h + 9}{ - 3 - 4} [/tex]

[tex] - 3 = \frac{h + 9}{ - 7} [/tex]

Cross multiply

That's

- 3(-7) = h + 9

21 = h + 9

h = 21 - 9

We have the final answer as

Hope this helps you

Answer:

The y-values repeat in various functions (for example: quadratic function: y=x²; y=4 for x=2 and for x=-2)  

Answer:

2 hrs, 24 min

Step-by-step explanation:

Sally:  in one hour, she can paint 1/4 of the room.

Joe: in one our, he can paint 1/6 of the room

Hour one: 1/4+1/6=3/12+2/12=5/12

1÷5/12=1*12/5=12/5

12/5= 2 & 2/5 hours, or 2.4 hours, or 2 hrs 24 minutes

Answer: 2.4 hours

Step-by-step explanation:

1/4 1/6

LCM

3/12+2/12=5/12 repricical 12/5 =2.4

Answer:

Step-by-step explanation:

23x +2 = 15x+48x+6

To solve for x group like terms

That's

Send the constants to the right side of the equation and those with variables to the left side

We have

23x - 15x - 48x = 6 - 2

Simplify

- 40x = 4

Divide both sides by -40

We have the final answer as

Hope this helps you

The order of a matrix is m×n where m is the number of rows and n is the number of columns.

can you count and find what are m and n here?

Answer:

Step-by-step explanation:

Number of rows X Number of columns

Rows = 3

Columns = 2

answer = 3x2

Answer:

slope - (2x)

y-intercept - (-1)

Step-by-step explanation:

-8x + 4y = - 4

4y = 8x - 4

y = 2x - 1

Answer:

7 divided by 4 is 1 ¾ as a fraction, or 1.75 as a decimal.

Step-by-step explanation:

Pls mark as brainliest answer

The calculated division of the numbers seven divided by 4 is 1 3/4

From the question, we have the following parameters that can be used in our computation:

seven divided by 4

When represented as an equation, we have

seven divided by 4 = 7/4

Divide 7 by 4

So, we have the following result

seven divided by 4 = 1 3/4

Using the above as a guide, we have the following:

the result is 1 3/4

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Answer:

3x +10y  is greater than or equal to 250.

Step-by-step explanation:

The question asks us to write an inequality which shows that both nylon and canvas added should be greater than or equal to 250.

Since we don't know the number of nylon backpacks and canvas backpacks the company makes, we used the variables "x" and "y" to represent the number of backpacks they made from each style.

Answer:

3n + 10c > 250

Step-by-step explanation:

I confirmed it in grandpoint

Answer:

x = 7

Step-by-step explanation:

4x + 5 = x + 26

4x - x = 26 - 5

3x = 21

x = 21/3

x = 7

Check:

4*7 + 5 = 7 + 26

28 + 5 = 33

Answer:

Option C.

Step-by-step explanation:

It is given that,

[tex]P(A)=\dfrac{1}{4}[/tex]

[tex]P(B)=\dfrac{13}{20}[/tex]

It is given that events A and B are mutually exclusive. It means they have no common elements.

[tex]P(A\cap B)=0[/tex]

We know that,

[tex]P(A\ or\ B)=P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

On substituting the values, we get

[tex]P(A\cup B)=\dfrac{1}{4}+\dfrac{13}{20}-0[/tex]

[tex]P(A\cup B)=\dfrac{5+13}{20}[/tex]

[tex]P(A\cup B)=\dfrac{18}{20}[/tex]

[tex]P(A\cup B)=\dfrac{9}{10}[/tex]

Therefore, the correct option is C.

The P (A or B) should be [tex]\frac{9}{10}[/tex]

Given that,

Based on the above information, the calculation is as follows:

[tex]= \frac{1}{4} + \frac{13}{20}\\\\= \frac{5+13}{20} \\\\= \frac{18}{20}\\\\= \frac{9}{10}[/tex]

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Hello there! :)

Answer:

[tex]\huge\boxed{x = 27}[/tex]

Given the equation:

3x - 4y = 65 where y = 4

Substitute in 4 for "y":

3x - 4(4) = 65

Simplify:

3x - 16 = 65

Add 16 to both sides:

3x - 16 + 16 = 65 + 16

3x = 81

Divide both sides by 3:

3x/3 = 81/3

x = 27.

Answer:

[tex]\frac{9}{100}[/tex]

Step-by-step explanation:

Given:

Number of red balls, n(R) = 3

Number of green balls, n(G) = 9

Number of yellow balls, n(Y) = 2

Number of orange balls, n(O) = 2

Number of purple balls, n(P) = 4

Two balls are drawn one at a time with replacement.

To find:

Probability of drawing a green ball and an orange ball ?

Solution:

Total number of balls, n(Total) = 3 + 9 + 2 + 2 + 4 = 20

Formula for probability of an event E is given as:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

Probability that a green ball is drawn at first:

[tex]P(Green) = \dfrac{\text{Number of Green balls}}{\text {Total number of Balls}}[/tex]

[tex]P(Green) = \dfrac{9}{20}[/tex]

Now, the ball is replaced , so total number of balls remain the same i.e. 20.[tex]P(Orange) = \dfrac{\text{Number of Orange balls}}{\text {Total number of Balls}}[/tex]

[tex]P(Orange) = \dfrac{2}{20} = \dfrac{1}{10}[/tex]

[tex]P(Green\ then\ orange) = P(Green) \times P(Orange)\\\Rightarrow P(Green\ then\ orange) = \dfrac{9}{10} \times \dfrac{1}{10}\\\Rightarrow P(Green\ then\ orange) = \bold{ \dfrac{9}{100} }[/tex]

distance of a point [tex](x,y)[/tex] from origin is $\sqrt{x^2+y^2}$

so distance is $\sqrt{(-15)^2+(8)^2}=\sqrt{225+64}=\sqrt{289}=17$

Answer:

Distance=17 units

Step-by-step explanation:

Coordinates of the origin: (0, 0)

Coordinates of the point in question: (-15, 8)

Distance formula for any two points [tex](x_1,y_1), (x_2,y_2)[/tex] on the plane:

[tex]distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\distance=\sqrt{(-15-0)^2+(8-0)^2}\\distance=\sqrt{(15)^2+(8)^2}\\distance=\sqrt{225+64} \\distance=\sqrt{289} \\distance=17[/tex]

Answer:

A=45cm^2

Step-by-step explanation:

A= h/2(b1 + b2) for trapezoid

A=(5/2(6+12))cm^2

A=(2.5(18))cm^2

A=45cm^2

Answer:

x = 15.9

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos theta = adj / hyp

cos 28 = 14/x

x  cos 28 = 14

x = 14 / cos 28

x=15.85598

Rounding to the nearest tenth

x = 15.9

Answer:

  the sides are different lengths as shown in the diagram

Step-by-step explanation:

Plotting the three points, you can see by "inspection" that the middle length side (PQ) is longer than the shortest side (QR) and shorter than the longest side (PR). You could use the distance formula to show this, or you can use a scale to measure the drawing.

A triangle with three unequal sides is a scalene triangle. ∆PQR is scalene.

Answer:

JK = 6.86

Step-by-step explanation:

The parameters given are;

LJ = 14

JM = 48

LM = 50

[tex]tan(\angle JML )= \dfrac{Opposite \ leg \ length}{Adjacent \ leg \ length} = \dfrac{LK}{JM} = \dfrac{14}{48} = \dfrac{7}{24}[/tex]

[tex]tan \left( \dfrac{7}{24} \right)= 16.26 ^{\circ }[/tex]

∠JML = 16.26°

Given that ∠JML is bisected by KM, we apply the angle bisector theorem which states that a ray that bisects an interior angle of a triangle bisects the opposite (bisected angle facing side) in the proportion of the ration of the other two sides of the triangle.

From the angle bisector theorem, we have;

LM/JM = LK/JK

50/48 = LK/JK................(1)

LK + KJ = 14.....................(2)

From equation (1), we have;

LK = 25/24×JK

25/24×KJ + JK = 14

JK×(25/24 + 1) = 14

JK × 49/24 = 14

JK = 14×24/49 = 48/7. = 6.86.

JK = 6.86

Answer:

37,139

Step-by-step explanation:

Given the following :

Population in 2002 = Initial population (P0) = 22,800

Growth rate (r) = 5% = 0.05

Growth in 2012 using the exponential growth function?

Time or period (t) = 2012 - 2002 = 10years

Exponential growth function:

P(t) = P0 * (1 + r) ^t

Where P(t) = population in t years

P(10) = 22800 * (1 + 0.05)^10

P(10) = 22800 * (1.05)^10

P(10) = 22800 * 1.62889

P(10) = 37138.797

P(10) = 37,139 ( to the nearest whole number)

Answer:

I hope this will help!

Step-by-step explanation:

Answer:

900 outfits

Step-by-step explanation:

You just have to multiply them all together :)

Answer:

-1, 4

Step-by-step explanation:

Answer:

Step-by-step explanation:

answer is (-1,4)

Answer:

All real numbers are solutions. 0=0

Step-by-step explanation:

(x+3)(x−5)=(x+3)(x−5)

Step 1: Simplify both sides of the equation.

x2−2x−15=x2−2x−15

Step 2: Subtract x^2 from both sides.

x2−2x−15−x2=x2−2x−15−x2

−2x−15=−2x−15

Step 3: Add 2x to both sides.

−2x−15+2x=−2x−15+2x

−15=−15

Step 4: Add 15 to both sides.

−15+15=−15+15

0=0

All real numbers are solutions.

Answer:

3x+11y-3

Step-by-step explanation:

Hey! So here is what you do to solve the problem-

Combine like terms:

(x) 5x-2x=3x

(y) 3y+8y=11y

(#) 7-10 =-3

So....

3x+11y-3 is your answer!

Hope this helps!:)

Answer:

4 is tenths (a) and 5 is hundredths (b)

Step-by-step explanation:

Now, 0.45

0 indicates the ones place (it comes before the decimal)

0.45 can also be written as:

0.4+0.05

= 4/10+5/100

what can we conclude from this?

we can say that 4 is in the tenths whilst 5 is in the hundredths.

therefore, a is 4 and b is 5.

Hope this helps you! :)

To build the fleet of ships, Astrid must consider each of the given rates (i.e.  the daily tons of wood, the sailors per ship, etc.). The available deliveries are enough to build ships that can accommodate at least 2100 sailors.

Given that:

Required quantities

[tex]Wood = 40\ tons[/tex]

[tex]Sailors = 300[/tex] per ship

Available quantities

[tex]Wood = 4\ tons[/tex] daily

[tex]Days = 100[/tex] at most

First, we calculate the total tons of woods Astrid can receive.

[tex]Total = Days \times Wood\ Available[/tex]

[tex]Total = 100 \times 4[/tex]

[tex]Total = 400\ tons[/tex] ---- in 100 days

Next, we calculate the number of ships that can be made from the 400 tons.

[tex]Ships = \frac{Total\ tons}{Wood\ Required}[/tex]

So, we have:

[tex]Ships = \frac{400}{40}[/tex]

[tex]Ships = 10[/tex]

This means that Astrid can build up to 10 ships

The number of sailors the ship can accommodate is:

[tex]Sailors = Ships \times Sailors\ per\ ship[/tex]

So, we have:

[tex]Sailors = 10 \times 300[/tex]

[tex]Sailors = 3000[/tex]

It means the 10 ships can accommodate 3000 sailors.

3000 sailors is greater than 2100 sailors.

So, we can conclude that she can build enough ship for the 2100 sailors.

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Answer:

280 tons

Step-by-step explanation:

:)

Answer:

Step 1: Isolate the absolute value expression.

Step2: Set the quantity inside the absolute value notation equal to + and - the quantity on the other side of the equation.

Step 3: Solve for the unknown in both equations.

Step 4: Check your answer analytically or graphically.

Step-by-step explanation:

Answer:

Rewrite the absolute value equation as two separate equations, one positive and the other negative

Solve each equation separately

After solving, substitute your answers back into original equation to verify that you solutions are valid

Write out the final solution or graph it as needed

Step-by-step explanation:

-5,3,-2,1 on a number line

<-|----|----|----|----|----|----|----|----|->

-5 -2 0 1 3